Field of the Invention
The present invention concerns a magnetic resonance method and system for generating a magnetic resonance image data record from a raw magnetic resonance data record with non-Cartesian data points.
Description of the Prior Art
In magnetic resonance tomography, a number of spatially encoded individual signals are recorded, in order to produce an image therefrom. A number of so-called post-processing steps are required, including a Fourier transformation of the acquired data in order to generate image data that constitutes a collection of data.
The detected signals are entered at points in a memory called k-space. For many imaging sequences, it is usual to enter the acquired data at respective k-space points in lines, so-called k-space lines. It is also possible to record k-space points individually, until, represented diagrammatically, all points of a rectangular, symmetrical grid are scanned. This type of data acquisition is referred to as Cartesian scanning or recording.
This procedure is disadvantageous particularly with point-by-point scanning of k-space, because it is time-consuming. It is also known to scan k-space spirally or radially. Here, a higher information density is obtained in the central region of k-space than in the peripheral areas. The central k-space lines make the highest contribution to the image contrast and the outer k-space lines make the highest contribution to the resolution, in other words showing the finer structures. Acceleration of the data acquisition results in a loss of information in the outer areas of k-space.
In order to be able to Fourier transform the spiral-shaped or radial k-space data to form a meaningful image data record, particularly using the accelerated Fourier transformation FFT, it is necessary to transfer k-space data into a Cartesian grid. This process is referred to as gridding or regridding. With gridding, the Cartesian k-space points are obtained according to the following formula:Mcart(x,y)={[(M*S*W)C]*R}−1C 
Here “M” refers to the magnetization of k-space, “S” the recording coordinates, “W” a weighting function, “C” a convolution (convolving) function and “R” the Cartesian grid.
Here the data of Cartesian k-space are eventually obtained by the adjacent, recorded data points being weighted and interpolated.
The weighting function defines how the measured k-space data flows into the calculated k-space data in order to balance the varying sampling density. The weighting function can be obtained for instance from the sampling coordinates “S” and the convolution function “C”, see Jackson et al. Selection of convolution function for Fourier Inversion using gridding. IEEE Trans Med Imaging 1991; 10: 473-480:
  W  =            1      ρ        =          1              S        ⊗        C            
In contrast, for interpolation purposes, a folding with a window function is performed. A known window function is the Hamming window. It is to be chosen in such a way that the Cartesian grid has no holes, but data points that are not too remote are taken into account.
In the two-dimensional case, the Cartesian grid is defined as:
      R    ⁡          (              x        ,        y            )        =            ∑      i        ⁢                  ∑        j            ⁢              δ        ⁡                  (                                    x              -              i                        ,                          y              -              j                                )                    
The projection thus results:Mcart(x,y)=Mconv(x,y)·R(x,y)
Once all steps of the gridding are completed, k-space with calculated or transformed Cartesian data points instead of radially or spirally distributed data points is achieved. The data can then be further processed with known post-processing steps such as baseline correction, zero filling, FFT, etc.
To avoid aliasing artifacts, it is necessary to position the field of view (FoV) such that the entire object to be examined is detected. Otherwise, foldovers occur. This means that more data than are actually necessary must be recorded, because normally only a limited area of the examination object is of interest. This additional data must be processed until an image is available. As a matter of course, areas can then be selected for representation in the image. Each is known as a region of interest or ROI. With three-dimensional data, such regions are each called a volume of interest or VOL
To optimize the acquisition of data, it is known to define the FoV and the number of k-space data points separately for each spatial direction. Moreover, the read direction is often positioned in the direction of the longest spatial extent in order to minimize the recording time. For instance, elongated examination objects enable k-space lines to lie in the direction of the longest extent.
With spiral trajectories, it is also known to design the FoV anisotropically, cf. King K., Spiral Scanning with Anisotropic Field of View, MRM, 39:448-456, 1989. Here k-space trajectory is adjusted to the object geometry. This procedure is also known for radial trajectories (Scheffler and Hennig, Reduced Circular Field-of-View Imaging, MRM, 40, 474-480, 1988) and radial trajectories (Larson et al., Anisotropic Field-of-Views in Radial Imaging, IEEE Trans Med Imaging, 27 (1), 47-57, 1991).
With all these methods, an improvement in the recording efficiency alone depends on the examination object having a primary direction, and therefore an adjustment to the field of view is possible. It is nevertheless still necessary to record the entire examination object in the complete excited area, because otherwise foldovers occur. This is particularly problematic with larger data records and interventional operations, since this slows down the image reconstruction. It is also not possible with all recording methods to perform these optimizations with an acceptable amount of hardware or computing outlay.